The present invention relates to a toothed belt having a plurality of elastic teeth formed of elastomeric material for meshing engagement with the teeth of a toothed pulley. More particularly, the invention relates to an improved tooth shape for such a toothed belt.
Trapezoid teeth are well known as a tooth shape for a toothed belt which is adapted to be trained around a plurality of toothed pulleys and constitute therewith a power transmitting device. In order to eliminate drawbacks of such trapezoid teeth, there have been proposed tooth shapes as disclosed in Japanese Patent Publication Nos. 52-20629, 56-37457, and 57-44866, Japanese Laid-Open Patent Publication No. 59-89852, Japanese Patent Publication Nos. 57-1714 and 57-60501.
In order for a toothed belt and a toothed pulley, hereinafter simply referred to as a "pulley," to mesh with each other without interference, the following three conditions must be met:
(1) the belt pitch line and the pulley pitch circle must be completely aligned with each other;
(2) the pitches of the toothed belt and the pulley must be completely equally divided, and be identical; and
(3) the belt teeth and the pulley teeth must be of such an optimum shape as to allow them to mesh with each other without interference for transmitting power.
The present invention is concerned with the problem indicated as (3) above, as it concerns the toothed belts disclosed in the aforesaid publications. As shown in FIG. 1, a trapezoid tooth 01 is generally used as a belt tooth. Such tooth shape, when it meshes with a pulley tooth 03, contacts the pulley tooth at a root fillet 02. Therefore, the root fillet is subjected to a concentrated stress in the form of shearing stress, and the belt tooth tends to suffer from localized damage.
To overcome this shortcoming, there has been proposed an arcuate tooth 04 which, as shown in FIG. 2, contacts a pulley tooth at a postion near the tooth tip when it meshes with the pulley tooth so that the tooth bears the force in its entirety (see Japanese Patent Publication Nos. 52-20629 and 57-44866). The arcuate tooth 04 can distribute the produced stress into the entire root portion of the tooth, and transmit the load uniformly at the tooth root portion to a load carrying member 05 on the belt pitch line. Consequently, the tooth root portion is less liable to break and is more durable.
There is also known an improved arcuate tooth in which the difference between the tooth shape and its envelope is made as small as possible so as to reduce the backlash of the arcuate tooth. Such a tooth shape is described in Japanese Laid-Open Patent Publication No. 59-89852.
When under low loads, the trapezoid tooth and the improved arcuate tooth are less deforable than the arcuate tooth. When subjected to high loads, however, the trapezoid tooth has been known to jump over the pulley tooth and the improved arcuate tooth has been known toslip against the pulley tooth, resulting in a large deformation. The arcuate tooth, on the other hand, is deformed at high loads to an extent which is substantially the same as that under the low loads.
When a high load is transmitted by a toothed belt, it is the general tendency for the belt to become more elongated; and for the belt teeth to be more deformed and to slip more on the pulley teeth. As a result, proper meshing engagement between the belt and pulley teeth is not effected, and the belt teeth tend to ride over the pulley teeth and are largely deformed.
Such behavior of the belt appears to depend on the pressure angle (.theta.) and the ratio (H/W) of the height (H) and the width (W) of the tooth shape.
As shown in FIG. 3, it can be assumed that, when a pulley tooth 07 and a belt tooth 06 are in mesh with each other, the force applied from the belt tooth 06 to the pulley tooth 07 at a point A is indicated by P; the coefficient of friction between the teeth by .mu.; the produced frictional force by F; and the pressure angle by .theta.. Then, the following equations (1), (2) and (3) are established: EQU P1=P cos .theta. (1) EQU P2=P sin .theta. (2) EQU F=.mu.P1=.mu.P cos .theta. (3)
In order to satisfy the condition P2&lt; for preventing the meshing teeth from slipping, the following inequality (4) must be met: EQU P sin .theta.&lt;.mu.P cos .theta. (4) EQU .thrfore. tan .theta.&lt;.mu. (5)
If it is assumed here that the coefficient of friction .mu. between a steel pulley and a rubber belt having teeth reinforced with woven fabric is 0.25 based on the coefficient of friction .mu.=0.21 between a steel pulley and a woven-fabric belt and the coefficient of friction .mu.=0.30 between a steel pulley and a rubber belt, then, from inequality (5), .theta.&lt;14.degree.. Therefore, in the described example the pressure angle .theta. must be smaller than 14 degrees in order to avoid tooth-to-tooth slippage.
Moreover, as shown in FIG. 4, while the belt tooth 06 was restrained on one side, a load (F=1 kg) was applied to the belt tooth 06 on the assumption that no slippage occurs between the teeth, and the belt tooth 06 was checked for the amount of lift (.delta.) due to deformation thereof. It was found that the amount of lift (.delta.) varies from tooth shape to tooth shape, and results, as were obtained from these experiments are indicated in Table 1. The differences between the amounts of lift (.delta.) greatly depend upon the ration (H/W) (see Table 1).
TABLE 1 ______________________________________ Tooth shape type Trapezoid Arcuate Improved arcuate tooth tooth tooth ______________________________________ Pressure angle (.theta.) 20.00 6.15 13.32 Ratio (H/W) 0.45 0.73 0.69 ______________________________________